Modified Stoney formula for determining stress within thin films on large-deformation isotropic circular plates

The Stoney formula is widely used to obtain residual stress in films on isotropic circular plates. However, in the case of large deformations, this formula produces significant errors because of the assumption of small deformations in its derivation. In this study, a modified Stoney formula that extends its scope of application to the nonlinear domain is proposed. A one-phase exponential decay function with a single coefficient p is used to relate the curvature of the substrate to the stress in the film. The coefficient p can be expressed as a function of the thickness, the diameter, Young’s modulus, and Poisson’s ratio of the circular plate. A linear fitting technique is applied to ascertain the relationship between the coefficient p and the aforementioned parameters. The modified Stoney formula is simple, yet accurate, and can be used to calculate the residual stress in the film directly from the measured curvature of isotropic circular plates with various dimensions and materials.